When's the earliest someone can become an AGR officer?

A 2/1 LT can pick up AGR positions if available, but do need to complete basic (officer) training. Branch school slotting can take up to a year. AGR officer slots are not AOC specific, the jobs are usually administrative that any branch could do. AGR is competitive.
OCS is competitive as well and not guaranteed that you'll get accepted. https://www.goarmy.com/careers-and-jobs/current-and-prior-service/advance-your-career/officer-candidate-school.html

You may as well be an active duty officer.

I think your AGR goal is an misinformed goal. I base this opinion on the fact you'd have to get into the USAR as an officer, get all trained up, and only then in a position to even be allowed to submit an AGR application. Then you have to take the first thing that comes along.

It can take up to a year to get selected for OCS depending on boards, how prepared you are to submit your packet, and just in general the administrative process of jumping through that hoop will vary. Then once selected, it could be another 6 months before you ship to even start training. Then training is 6 months and you finally get to your Reserve unit. It will be your reserve unit that will send you to your Branch school, and that all depends on you and your school timing. It took me nearly a year to get to Branch training and once there it was another 4 months. Then at that moment of graduation from branch school I am now fully qualified to do the job of a 2LT, and the absolute least experienced to do the job.

Then lets say you finally get through all that, and you think the USAR isn't for you. That's going to suck because you are on the hook for 8 years, AGR job or not.

I wouldn't enter AGR until I was a CPT with my captain's course behind me.

Let's say you do jump all the hoops and become a USAR 2LT. While at your unit you will be best positioned to seek out an AGR Officer mentor.

Now, on your way to an AGR path you will be presented with various chances for extended orders. My e-mail was filled with General Aide positions, XO positions for Basic Training Companies, and Company Commander positions for Basic Training (would be an interesting experience at the least).

I think if you hit AGR as a LT you will get over worked, will have to exit the ARG program to get company command time, and taking your Captain's Course would be hard as well.

I'd say become a USAR 2LT volunteer for the various chances to go on extended orders. Get your command time out of the way, and knock out the captain's course before you apply AGR so by time you are in the AGR you are in a position to get promoted to Major (which could be 7 years away from the start of CPT) and competitively because you would have your command time done, your Captains course, and various positions of learning experience.

From where you sit now to employment as an AGR Officer/LT

3-5 years